all simulations that require semi-random calculations change when you change the processors, differences in the floating point units (mostly) are responsible. It's the reason you should be using all the same chips in a render farm.
You moved from Xeon to Xeon but it's still a change of processor generation and it's doubtful (impossible) they would be the same. If you can use the old machine still you could bake the dynamics there and render on the new one.